Showing papers on "Minimum weight published in 2020"
TL;DR: This work shows that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product, and improves upon previous quantum decoders based on belief propagation, and approaches the performance of the minimum weight perfect matching algorithm.
Abstract: We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the decoder applied to three families of hypergraph product code: topological codes, fixed-rate random codes and a new class of codes that we call semi-topological codes. Our new code families share properties of both topological and random hypergraph product codes, with a construction that allows for a finely-controlled trade-off between code threshold and stabilizer locality. Our results indicate thresholds across all three families of hypergraph product code, and provide evidence of exponential suppression in the low error regime. For the Toric code, we observe a threshold in the range $9.9\pm0.2\%$. This result improves upon previous quantum decoders based on belief propagation, and approaches the performance of the minimum weight perfect matching algorithm. We expect semi-topological codes to have the same threshold as Toric codes, as they are identical in the bulk, and we present numerical evidence supporting this observation.
48 citations
TL;DR: An original revisitation of the thrust line analysis is presented, within a theoretical framework which unifies the classical equilibrium formulations of masonry arches and enlightens the relationships among them.
21 citations
TL;DR: The methodology proposed in this paper provides an efficient way to achieve optimal design for other kinds of structures and illustrates that to obtain the maximal stiffness based on the optimal weight, the thickness of the cube-shaped cross sections tends to be the minimum, whereas the diameter to beThe maximum.
20 citations
TL;DR: The proposed algorithm combines local search with repair procedure based on the mind of reinforcement learning with results that display that LSRR outperforms the previous MWIDS algorithms significantly.
17 citations
TL;DR: In this paper, the authors apply deep reinforcement learning techniques to design high threshold decoders for the toric code under uncorrelated noise, and observe that the agent implements a policy similar to that of minimum weight perfect matchings even though no bias towards any policy is given a priori.
16 citations
TL;DR: In this article, a new practical analytical approach has been developed in order to reach the optimal fiber orientation in design of fiber reinforced polymer pressure vessels (FRPPVs) subjected to hydrostatic pressure.
Abstract: A new practical analytical approach has been developed in order to reach the optimal fiber orientation in design of fiber reinforced polymer pressure vessels (FRPPVs) subjected to hydrostatic pressure. The method consists of analytical solutions along with optimizing process in which different decisive factors such as buckling pressure, weight, failure of fiber and matrix, thickness, number and angle of layers are considered as problem constraints. In analytical part, besides the buckling analysis, Tsai-Wu and Hashin failure criteria are employed to analyze the failure of the structure. Then, the genetic algorithm (GA), as a robust optimization method, is applied to achieve the optimal orientation pattern with minimum weight and maximum buckling load. In addition, the impact of mapped fitness function in optimization process is exclusively analyzed. Next, to validate the reliability and effectiveness of the proposed approach, two different experimental methods, including the strain gauge and volume control methods, are performed and measured buckling pressure is compared with the analytical results. The results indicated that using the proposed approach, critical buckling load increases by 40% while the weight is reduced by 15%, simultaneously.
16 citations
TL;DR: In this paper, the authors proposed a novel method for topology optimization of elastoplastic structures subjected to stress constraints, where the classical variational principles of plasticity and the functor-oriented programming technique are applied in topology design.
Abstract: This study is devoted to a novel method for topology optimization of elastoplastic structures subjected to stress constraints. It should be noted that in spite of the classical solutions of the different type of elastoplastic topology problems are more than 70 years old, the integration of the Prandtl-Reuss constitutive equations into the topology optimization process is not very often investigated in the last three decades. In the presented methodology where the classical variational principles of plasticity and the functor-oriented programming technique are applied in topology design, the aim is to find a minimum weight structure which is able to carry a given load, fulfills the allowable stress limit, and is made of a linearly elastic, perfectly plastic material. The optimal structure is found in an iterative way using only a stress intensity distribution and a return mapping algorithm. The method determines representative stresses at every Gaussian point, averages them inside every finite element using the von Mises yield criterion, and removes material proportionally to the stress intensities in individual finite elements. The procedure is repeated until the limit load capacity is exceeded under a given loading. The effectiveness of the methodology is illustrated with three numerical examples. Additionally, different topologies are presented for a purely elastic and an elastoplastic material, respectively. It is also demonstrated that the proposed method is able to find the optimal elastoplastic topology for a problem with a computational mesh of the order of tens of thousands of finite elements.
14 citations
TL;DR: It is found that the maximum likelihood (ML) performance of a simple CRC-polar concatenated scheme can approach the normal approximation of the finite blocklength capacity.
Abstract: In this letter, we explore the performance limits of short polar codes and find that the maximum likelihood (ML) performance of a simple CRC-polar concatenated scheme can approach the normal approximation of the finite blocklength capacity. To explore the performance limits, CRC-polar concatenated codes are first optimized according to the minimum weight distribution. Then, CRC-aided hybrid decoding (CA-HD) algorithm with two steps is proposed to approach the ML performance. In the first step, the received sequence is decoded by the adaptive successive cancellation list (ADSCL) decoding. In the second step, the CRC bits of the survival paths in ADSCL are recalculated and CRC-aided sphere decoding with a reasonable initial radius calculated by the newly survival paths is used. The simulation results show that CRC-polar concatenated code with codeword length 128 and code rate 1/2 can achieve within about 0.025 dB of the normal approximation of the finite blocklength capacity at the block error rate 10−3.
13 citations
Posted Content•
TL;DR: In this article, Assmus-mattson type theorems for codes and lattices were given for binary doubly even self-dual codes and even unimodular lattices.
Abstract: In the present paper, we give Assmus--Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m with minimum norm 2m provides a spherical 3-design. We remark that some of such codes and lattices give t-designs for higher t. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24m with minimum weight 4m. Ternary and quaternary analogues are also given.
9 citations
TL;DR: This article studies the efficacy of the Metropolis algorithm for the minimum-weight codeword problem and provides both theoretical and experimental justification to show why the generator space is a worthwhile search space for this problem.
Abstract: This article studies the efficacy of the Metropolis algorithm for the minimum-weight codeword problem . The input is a linear code $C$ given by its generator matrix and our task is to compute a nonzero codeword in the code $C$ of least weight. In particular, we study the Metropolis algorithm on two possible search spaces for the problem: 1) the codeword space and 2) the generator space . The former is the space of all codewords of the input code and is the most natural one to use and hence has been used in previous work on this problem. The latter is the space of all generator matrices of the input code and is studied for the first time in this article. In this article, we show that for an appropriately chosen temperature parameter the Metropolis algorithm mixes rapidly when either of the search spaces mentioned above are used. Experimentally, we demonstrate that the Metropolis algorithm performs favorably when compared to previous attempts. When using the generator space, the Metropolis algorithm is able to outperform the previous algorithms in most of the cases. We have also provided both theoretical and experimental justification to show why the generator space is a worthwhile search space to use for this problem.
9 citations
TL;DR: In this study, a comprehensive investigation was conducted into the solution of the spur gear design problem in metaheuristic optimization methods, and it was shown that the new methods demonstrated significantly improved performance in solving the Gear design problem compared to existing methods.
Abstract: The design of gears with a minimum weight is an optimization problem that has been widely discussed in the literature. Various recent metaheuristic optimization methods, along with the conventional...
TL;DR: This research was derived from the experimental observation that hydraulic actuators are positioned on machines that are subjected to movements and whose dynamic actions, the accelerations, are very high; it is acceptable to think of an actuator for an anthropomorphic robot.
Abstract: This research was derived from the experimental observation that hydraulic actuators are positioned on machines that are subjected to movements and whose dynamic actions, the accelerations, are very high; it is acceptable to think of an actuator for an anthropomorphic robot. From this point of view, the weight of the actuator plays a fundamental role in the performance of the machine. In order to face this problem, a real hydraulic cylinder has been designed (for use on an earth moving machine) both analytically (adopting the theories of continuous mechanics) and numerically through finite element analysis. The results obtained were then generalized by determining functions that in relation to specific values of the variables, such as working pressure, allow one to determine the minimum weight of the component and its geometric configuration. The functions also made it possible to identify the most significant contributions to the overall weight of the component and therefore the elements on which to focus the subsequent lightening process. In particular, the greatest contribution is made by obtaining relations that are completely general and therefore adaptable to different case studies.
TL;DR: In this paper, it was shown that any ternary Euclidean (resp. quaternary Hermitian) linear complementary dual [n, k ] code contains a Euclideans (resp., Hermitians) LHD subcode for 2 ≤ k ≤ n.
15 Jul 2020
TL;DR: The improved memetic algorithm called MSSAS is presented, which combines probability-based dynamic optimization (PDO) as well as a local search phase named C_LS (to seek high-quality local optima by combining the idea of constrained-based two-level configuration checking strategy and tabu mechanism).
Abstract: The minimum weight vertex independent dominating set (MWVIDS) problem is an important version of the minimum independent dominating set. The MWVIDS problem has a number of applications in many fields. However, the MWVIDS problem is known to be NP-hard and thus computationally challenging. In this work, we present the improved memetic algorithm called MSSAS for solving the MWVIDS problem. The proposed MSSAS algorithm combines probability-based dynamic optimization (PDO) (to generate good and diverse offspring solutions by assembling elements of existing good solutions) as well as a local search phase named C_LS (to seek high-quality local optima by combining the idea of constrained-based two-level configuration checking strategy and tabu mechanism). The extensive results on popular DIMACS and BHOLIB benchmarks demonstrate that MSSAS competes favorably with the state-of-the-art algorithms. In addition, we analyze the benefits of the newly raised components including two above proposed ideas with our memetic framework. It is worth mentioning that the combination of both components has excellent effects for the MWVIDS problem.
Posted Content•
TL;DR: Three enumeration methods are proposed that can exactly enumerate all the codewords with the minimum Hamming weight and show that the SCREM has about $10^6$ times complexity reduction compared with the existing methods at code length 128 and the PC-SCEM can be used to design high-performance CRC-polar concatenated codes.
Abstract: In this paper, the minimum weight distributions (MWDs) of polar codes and concatenated polar codes are exactly enumerated according to the distance property of codewords. We first propose a sphere constraint based enumeration method (SCEM) to analyze the MWD of polar codes with moderate complexity. The SCEM exploits the distance property that all the codewords with the identical Hamming weight are distributed on a spherical shell. Then, based on the SCEM and the Plotkin's construction of polar codes, a sphere constraint based recursive enumeration method (SCREM) is proposed to recursively calculate the MWD with a lower complexity. Finally, we propose a parity-check SCEM (PC-SCEM) to analyze the MWD of concatenated polar codes by introducing the parity-check equations of outer codes. Moreover, due to the distance property of codewords, the proposed three methods can exactly enumerate all the codewords belonging to the MWD. The enumeration results show that the SCREM can enumerate the MWD of polar codes with code length up to $2^{14}$ and the PC-SCEM can be used to optimize CRC-polar concatenated codes.
TL;DR: A new extension theorem for ternary linear codes is given and it is proved the non-existence of [ 512, 6, 340 ] 3 code, which is a new result.
TL;DR: In this article, a new structure of product codes formed by combining two polar codes is presented, and the encoding performance of these codes is verified by implementing an exhaustive search algorithm, which determines their minimum weight specifications.
Abstract: This paper presents a new structure of product codes formed by combining two polar codes. The encoding performance of these codes is verified by implementing an exhaustive search algorithm, which determines their minimum weight specifications. Conducted analysis and simulations confirm that with the equal code length and rate, the newly proposed codes outperform the conventional polar codes in high energy per bit-to-noise ratios ( dB). This is concluded from punctured and nonpunctured product codes.
TL;DR: In this article, a method of weight optimization of a composite hat stiffened panel of a transport aircraft wing meeting the strength and buckling design constraints for different stringer spacings was proposed.
TL;DR: This paper improves the result by showing that ( k − 1 ) -approximation can be achieved when the girth requirement is relaxed from k to 2 k / 3 .
Posted Content•
TL;DR: The real multilinear polynomial for the Boolean function which determines if a graph G \subseteq K_{n,n} contains one of these minimum weight perfect matchings is given.
Abstract: In a recent paper, Beniamini and Nisan gave a closed-form formula for the unique multilinear polynomial for the Boolean function determining whether a given bipartite graph $G \subseteq K_{n,n}$ has a perfect matching, together with an efficient algorithm for computing the coefficients of the monomials of this polynomial. We give the following generalization: Given an arbitrary non-negative weight function $w$ on the edges of $K_{n,n}$, consider its set of minimum weight perfect matchings. We give the real multilinear polynomial for the Boolean function which determines if a graph $G \subseteq K_{n,n}$ contains one of these minimum weight perfect matchings.
TL;DR: In this paper, the dynamic sizing optimization problem of a truss structure for its weight minimization with a constraint of the frequency response function (FRF) over a certain frequency band was studied.
Abstract: The dynamic sizing optimization problem of a truss structure is studied for its weight minimization with a constraint of the frequency response function (FRF) over a certain frequency bandw...
24 Oct 2020
TL;DR: An improved NSGA-II algorithm based on greedy heuristics to tackle the minimum weight minimum connected dominating set problem and shows a significant improvement of the approach with respect to the hypervolume indicator, run-time, and quality of solutions.
Abstract: Most real-world problems are multiobjective in nature and considerable research efforts have been devoted to propose efficient multiobjective optimization approaches. Nondominated sorting genetic algorithm II (NSGA-II) is one of the well-known algorithms for this purpose which is based on a fast nondominated sorting procedure and an elitist selection strategy. This paper presents an improved NSGA-II algorithm (I-NSGA-II) based on greedy heuristics to tackle the minimum weight minimum connected dominating set problem. To make a trade-off between the size of the connected dominating set and its total weight, two objectives are considered, namely the minimization of the size and the minimization of the total edge-weight. The performance of I-NSGA-II is evaluated on a set of test problem instances with different sizes. Computational experiments show a significant improvement of our approach over NSGA-II with respect to the hypervolume indicator, run-time, and quality of solutions.
TL;DR: It is shown that MWtCP is NP-hard, APX-hard in the general case, and a 2-approximation algorithm that runs in O(n) for the metric case and has 1+ 1 t -approximating performance guarantee for the ultrametric subclass of instances is presented.
Abstract: The Minimum Weight t-partite Clique Problem MWtCP is the problem of finding a t-clique with minimum weight in a complete edgeweighted t-partite graph. The motivation for studying this problem is its potential in modelling the problem of identifying sets of commonly existing putative co-regulated, co-expressed genes, called gene clusters. In this paper, we show that MWtCP is NP-hard, APX-hard in the general case. We also present a 2-approximation algorithm that runs in O(n) for the metric case and has 1+ 1 t -approximation performance guarantee for the ultrametric subclass of instances. We further show how relaxing or tightening the application of the metricity property affects the approximation ratio. Finally insights on the application MWtCP to gene cluster discovery are presented. Submitted: August 2018 Reviewed: January 2019 Revised: March 2019 Reviewed: July 2019 Revised: September 2019 Accepted: March 2020 Final: March 2020 Published: April 2020 Article type: Regular Paper Communicated by: F. Vandin E-mail addresses: gasolano@up.edu.ph (Geoffrey Solano) guillaume.blin@labri.fr (Guillaume Blin) mathieu.raffinot@labri.fr (Mathieu Raffinot) jhoiclemente@gmail.com (Jhoirene Clemente) jdlcaro@up.edu.ph (Jaime Caro) 172 Solano, Blin, Raffinot, Clemente & Caro Approximability of MWtCP
Posted Content•
TL;DR: A dynamic programming algorithm is proposed to solve the problem of bounding non-minimum weight differentials (EDP) and linear hulls (ELP) in 2-round LSX-cipher and the exact value of the maximum expected differential (linear) probability was computed for this cipher.
Abstract: This article describes some approaches to bounding non-minimum weight differentials (EDP) and linear hulls (ELP) in 2-round LSX-cipher. We propose a dynamic programming algorithm to solve this problem. For 2-round Kuznyechik the nontrivial upper bounds on all differentials (linear hulls) with 18 and 19 active Sboxes was obtained. These estimates are also holds for other differentials (linear hulls) with a larger number of active Sboxes. We obtain a similar result for 2-round Khazad. As a consequence, the exact value of the maximum expected differential (linear) probability (MEDP/MELP) was computed for this cipher.
01 Jan 2020
TL;DR: This research work, hybrid racing vehicle is optimally designed such that the overall weight is reduced and the starting torque is increased and shows feasibility of implementing the proposed design in practice for manufacturing the hybrid racing cars.
Abstract: The key issues associated with the hybrid racing car are low starting torque, lower acceleration and more weight. In this research work, hybrid racing vehicle is optimally designed such that the overall weight is reduced and the starting torque is increased. This is achieved by designing sustainable and safe chassis with minimum members. Further, materials that have maximum strength with minimum weight is identified. The simulation study is performed in NX-CAD software. It can be observed from the results that the weight is reduced by around 11.4 %. Moreover, suitable motor, battery, steering, suspension and braking system are identified for a hybrid racing car. This shows feasibility of implementing the proposed design in practice for manufacturing the hybrid racing cars.
TL;DR: This paper presents an exact algorithm with a runtime O(mn 2) for CMST when the edge length is restricted to 0 and 1 based on combining the local search method and the developed bicameral edge replacement approach.
Abstract: For a given undirected graph with each edge associated with a weight and a length, the constrained minimum spanning tree (CMST) problem aims to compute a minimum weight spanning tree with total length bounded by a given fixed integer $$L\in {\mathbb {Z}}^{+}$$. In the paper, we first present an exact algorithm with a runtime $$O(mn^{2})$$ for CMST when the edge length is restricted to 0 and 1 based on combining the local search method and our developed bicameral edge replacement approach. Then we extend the algorithm to solve a more general case when the edge length is restricted to 0, 1 and 2 via iteratively improving a feasible solution of CMST towards an optimum solution. At last, numerical experiments are carried out to validate the practical performance of the proposed algorithms by comparing with previous algorithms as baselines.
TL;DR: This paper considers the LDPC codes defined by taking the incidence matrix and its transpose as parity-check matrices and proves a conjecture of Vandendriessche that the code is generated by words of minimum weight called plane words.
TL;DR: This work proposes a cutset-based integer linear programming formulation, provides different linear relaxations to reduce the number of variables in the model and solves the reduced model using a branch-and-cut approach.
21 Jun 2020
TL;DR: A harddecision iterative decoding algorithm is proposed, which can correct errors beyond half of the code’s minimum Hamming distance and is realized with polynomial multiplication and integer comparisons, which are hardware-friendly.
Abstract: This paper proposes a novel shift-sum decoding scheme for non-binary cyclic codes. Using minimum-weight dual codewords and their cyclic shifts, a reliability measure can be yielded as an indicator for the error position and the error magnitude. Based on this shift-sum decoding concept, a harddecision iterative decoding algorithm is proposed, which can correct errors beyond half of the code’s minimum Hamming distance. By utilizing reliability information from the channel, a soft-decision iterative decoding algorithm is further introduced to improve the decoding performance. These two shift-sum based iterative decoding algorithms are realized with polynomial multiplication and integer (or real number) comparisons, which are hardware-friendly. Simulation results on Reed-Solomon codes and non-binary BCH codes show the decoding potential of the proposed algorithms.
22 May 2020
TL;DR: In this article, the design of plane and spatial truss structures are optimized by a popular metaheuristic optimization technique named teaching-learning-based optimization (TLBO), which is preferred by many researches to find the minimum weight of truss structure considering size and/or shape design variables which are the truss element's cross-sectional area and joint coordinates of the geometry of the trussedes for the size and shape optimization, respectively.
Abstract: Metaheuristic algorithm is preferred by the many researches to find the minimum weight of truss structures considering size and/or shape design variables which are the truss element's cross-sectional area and joint coordinates of the geometry of the trusses for the size and shape optimization, respectively. The design of plane and spatial truss structures are optimized by a popular metaheuristic optimization technique named Teaching-Learning-Based Optimization (TLBO). Finite element analyses of structures and optimization process were carried out by the computer program coded in MATLAB visually developed by the authors. Two benchmark problems (37-bar, and 72-bar) taken from literature were optimized and the optimal solutions belong this paper were compared with previous studies.